= Solution
Taking the <partial trace> over the left atom in the <singlet state> gives the right-hand <reduced density matrix>
$$
(\rho_R)_{ss'}=\sum_{a=\uparrow,\downarrow}\langle a,s|\rho_D|a,s'\rangle,
\qquad\boxed{\rho_R=\frac12\begin{pmatrix}1&0\\0&1\end{pmatrix}=\frac I2.}
$$
Thus every measurement on the right stream alone has the same statistics as B or C. The joint <pure state> is compatible with locally <mixed states>; the correlations reside in the full <density operator>.
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